Just a blog by a guy who's a retired math teacher

As you probably know, a handful of agricultural researchers and economists have come up with extremely complicated “Value-Added” Measurement (VAM) systems that purport to be able to grade teachers’ output exactly.

These economists (Hanushek, Chetty and a few others) claim that their formulas are magically mathematically able to single out the contribution of every single teacher to the future test scores and total lifetime earnings of their students 5 to 50 years into the future. I’m not kidding.

Of course, those same economists claim that the teacher is the single most important variable affecting their student’s school and trajectories – not family background or income, nor peer pressure, nor even whole-school variables. (Many other studies have shown that the effect of any individual teacher, or all teachers, is pretty small – from 1% to 14% of the entire variation, which corresponds to what I found during my 30 years of teaching … ie, not nearly as much of an impact as I would have liked [or feared], one way or another…)

Diane Ravitch has brought to my attention an important study by Stuart Yen at UMinn that (once again) refutes those claims, which are being used right now in state after state and county after county, to randomly fire large numbers of teachers who have tried to devote their lives to helping students.

According to the study, here are a few of the problems with VAM:

1. As I have shown repeatedly using the New York City value-added scores that were printed in the NYTimes and NYPost, teachers’ VAM scores vary tremendously over time. (More on that below; note that if you use VAM scores, 80% of ALL teachers should be fired after their first year of teaching) Plus RAND researchers found much the same thing in North Carolina. Also see this. And this.

2. Students are not assigned randomly to teachers (I can vouch for that!) or to schools, and there are always a fair number of students for whom no prior or future data is available, because they move to other schools or states, or drop out, or whatever; and those students with missing data are NOT randomly distributed, which pretty makes the whole VAM setup an exercise in futility.

3. The tests themselves often don’t measure what they are purported to measure. (Complaints about the quality of test items are legion…)

Here is an extensive quote from the article. It’s a section that Ravitch didn’t excerpt, so I will, with a few sentences highlighted by me, since it concurs with what I have repeatedly claimed on my blog:

A largely ignored problem is that true teacher performance, contrary to the main assumption underlying current VAM models, varies over time (Goldhaber & Hansen, 2012). These models assume that each teacher exhibits an underlying trend in performance that can be detected given a sufficient amount of data. The question of stability is not a question about whether average teacher performance rises, declines, or remains flat over time.

The issue that concerns critics of VAM is whether individual teacher performance fluctuates over time in a way that invalidates inferences that an individual teacher is “low-” or “high-” performing.

This distinction is crucial because VAM is increasingly being applied such that individual teachers who are identified as low-performing are to be terminated. From the perspective of individual teachers, it is inappropriate and invalid to fire a teacher whose performance is low this year but high the next year, and it is inappropriate to retain a teacher whose performance is high this year but low next year.

Even if average teacher performance remains stable over time, individual teacher performance may fluctuate wildly from year to year.(my emphasis – gfb)

However, this hypothesis was rejected by Goldhaber and Hansen (2012), who investigated the stability of teacher performance in North Carolina using data spanning 10 years and found that much of a teacher’s true performance varies over time due to unobservable factors such as effort, motivation, and class chemistry that are not easily captured through VAM. This invalidates the assumption of stable teacher performance that is embedded in Hanushek’s (2009b) and Gordon et al.’s (2006) VAM-based policy proposals, as well as VAM models specified by McCaffrey et al. (2009) and Staiger and Rockoff (2010) (see Goldhaber & Hansen, 2012, p. 15).

The implication is that standard estimates of impact when using VAM to identify and replace low-performing teachers are significantly inflated (see Goldhaber & Hansen, 2012, p. 31).

As you also probably know, the four main ‘tools’ of the billionaire-led educational DEform movement are:

* firing lots of teachers

* breaking their unions

* closing public schools and turning education over to the private sector

* changing education into tests to prepare for tests that get the kids ready for tests that are preparation for the real tests

They’ve been doing this for almost a decade now under No Child Left Untested and Race to the Trough, and none of these ‘reforms’ have shown to make any actual improvement in the overall education of our youth.

To depart from my text, I want to start by proposing a solution: look hard at the collaborative assessment model being used a few miles away in Montgomery County [MD] and follow the advice of Edwards Deming.

Even though I personally retired before [the establishment of the] IMPACT [teacher evaluation system], I want to use statistics and graphs to show that the Value-Added measurements that are used to evaluate teachers are unreliable, invalid, and do not help teachers improve instruction. To the contrary: IVA measurements are driving a number of excellent, veteran teachers to resign or be fired from DCPS to go elsewhere.

Celebrated mathematician John Ewing says that VAM is “mathematical intimidation” and a “modern, mathematical version of the Emperor’s New Clothes.”

I agree.

One of my colleagues was able to pry the value-added formula [used in DC] from [DC data honcho] Jason Kamras after SIX MONTHS of back-and-forth emails. [Here it is:]

One problem with that formula is that nobody outside a small group of highly-paid consultants has any idea what are the values of any of those variables.

In not a single case has the [DCPS] Office of Data and Accountability sat down with a teacher and explained, in detail, exactly how a teacher’s score is calculated, student by student and class by class.

Nor has that office shared that data with the Washington Teachers’ Union.

I would ask you, Mr. Catania, to ask the Office of Data and Accountability to share with the WTU all IMPACT scores for every single teacher, including all the sub-scores, for every single class a teacher has.

Now let’s look at some statistics.

My first graph is completely random data points that I had Excel make up for me [and plot as x-y pairs].

Notice that even though these are completely random, Excel still found a small correlation: r-squared was about 0.08 and r was about 29%.

Now let’s look at a very strong case of negative correlation in the real world: poverty rates and student achievement in Nebraska:

The next graph is for the same sort of thing in Wisconsin:

Again, quite a strong correlation, just as we see here in Washington, DC:

Now, how about those Value-Added scores? Do they correlate with classroom observations?

Mostly, we don’t know, because the data is kept secret. However, someone leaked to me the IVA and classroom observation scores for [DCPS in] SY 2009-10, and I plotted them [as you can see below].

I would say this looks pretty much no correlation at all. It certainly gives teachers no assistance on what to improve in order to help their students learn better.

And how stable are Value-Added measurements [in DCPS] over time? Unfortunately, since DCPS keeps all the data hidden, we don’t know how stable these scores are here. However, the New York Times leaked the value-added data for NYC teachers for several years, and we can look at those scores to [find out]. Here is one such graph [showing how the same teachers, in the same schools, scored in 2008-9 versus 2009-10]:

That is very close to random.

How about teachers who teach the same subject to two different grade levels, say, fourth-grade math and fifth-grade math? Again, random points:

One last point:

Mayor Gray and chancellors Henderson and Rhee all claim that education in DC only started improving after mayoral control of the schools, starting in 2007. Look for yourself [in the next two graphs].

Notice that gains began almost 20 years ago, long before mayoral control or chancellors Rhee and Henderson, long before IMPACT.

To repeat, I suggest that we throw out IMPACT and look hard at the ideas of Edwards Deming and the assessment models used in Montgomery County.

Testimony of Guy Brandenburg, retired DCPS mathematics teacher before the DC City Council Committee on Education Roundtable, December 14, 2013 at McKinley Tech

Hello, Mr. Catania, audience members, and any other DC City Council members who may be present. I am a veteran DC math teacher who began teaching in Southeast DC about 35 years ago, and spent my last 15 years of teaching at Alice Deal JHS/MS. I taught everything from remedial 7th grade math through pre-calculus, as well as computer applications.

Among other things, I coached MathCounts teams at Deal and at Francis JHS, with my students often taking first place against all other public, private, and charter schools in the city and going on to compete against other state teams. As a result, I have several boxes full of trophies and some teaching awards.

Since retiring, I have been helping Math for America – DC (which is totally different from Teach for America) in training and mentoring new but highly skilled math teachers in DC public and charter schools; operating a blog that mostly concerns education; teaching astronomy and telescope making as an unpaid volunteer; and also tutoring [as a volunteer] students at the school closest to my house in Brookland, where my daughter attended kindergarten about 25 years ago.

But this testimony is not about me; as a result, I won’t read the previous paragraphs aloud.

My testimony is about how the public is being deceived with bogus statistics into thinking things are getting tremendously better under mayoral control of schools and under the chancellorships of Rhee and Henderson.

In particular, I want to show that the Value-Added measurements that are used to evaluate teachers are unreliable, invalid, and do not help teachers improve their methods of instruction. To the contrary: IVA measurements are driving a number of excellent, veteran teachers to resign or be fired from DCPS to go elsewhere.

I will try to show this mostly with graphs made by me and others, because in statistics, a good scatter plot is worth many a word or formula.

John Ewing, who is the president of Math for America and is a former executive director of the American Mathematical Society, wrote that VAM is “mathematical intimidation” and not reliable. I quote:

In case you were wondering how the formula goes, this is all that one of my colleagues was able to pry from Jason Kamras after SIX MONTHS of back-and-forth emails asking for additional information:

One problem with that formula is that nobody outside a small group of highly-paid consultants has any idea what are the values of any of those variables. What’s more, many of those variables are composed of lists or matrices (“vectors”) of other variables.

In not a single case has the Office of Data and Accountability sat down with a teacher and explained, in detail, exactly how a teachers’ score is calculated, student by student, class by class, test score by test score.

Nor has that office shared that data with the Washington Teachers’ Union.

It’s the mathematics of intimidation, lack of accountability, and obfuscation.

I would ask you, Mr. Catania, to ask the Office of Data and Accountability to share with the WTU all IMPACT scores for every single teacher, including all the sub-scores, such as those for IVA and classroom observations.

To put a personal touch to my data, one of my former Deal colleagues shared with me that she resigned from DCPS specifically because her IVA scores kept bouncing around with no apparent reason. In fact, the year that she thought she did her very best job ever in her entire career – that’s when she earned her lowest value-added score. She now teaches in Montgomery County and recently earned the distinction of becoming a National Board Certified teacher – a loss for DCPS students, but a gain for those in Maryland.

Bill Turque of the Washington Post documented the case of Sarah Wysocki, an excellent teacher with outstanding classroom observation results, who was fired by DCPS for low IVA scores. She is now happily teaching in Virginia. I am positive that these two examples can be multiplied many times over.

Now let’s look at some statistics. As I mentioned, in many cases, pictures and graphs speak more clearly than words or numbers or equations.

My first graph is of completely random data points that should show absolutely no correlation with each other, meaning, they are not linked to each other in any way. I had my Excel spreadsheet to make two lists of random numbers, and I plotted those as the x- and y- variables on the following graph.

I asked Excel also to draw a line of best fit and to calculate the correlation coefficient R and R-squared. It did so, as you can see, R-squared is very low, about 0.08 (eight percent). R, the square root of R-squared, is about 29 percent.

Remember, those are completely random numbers generated by Excel.

Now let’s look at a very strong correlation of real numbers: poverty rates and student achievement in a number of states. The first one is for Nebraska.

R would be about 94% in this case – a very strong correlation indeed.

The next one is for Wisconsin:

Again, quite a strong correlation – a negative one: the poorer the student body, the lower the average achievement, which we see repeated in every state and every country in the world. Including DC, as you can see here:

Now, how about those Value-Added scores? Do they correlate with classroom observations?

Mostly, we don’t know, because the data is kept secret. However, someone leaked to me the IVA and classroom observation scores for all DCPS teachers for SY 2009-10, and I plotted them. Is this a strong correlation, or not?

I would say this looks pretty much like no correlation at all. What on earth are these two things measuring? It certainly gives teachers no assistance on what to improve in order to help their students learn better.

And how stable are Value-Added measurements over time? If they are stable, that would mean that we might be able to use them to weed out the teachers who consistently score at the bottom, and reward those who consistently score at the top.

Unfortunately, since DCPS keeps all the data hidden, we don’t exactly know how stable these scores are here. However, the New York Times leaked the value-added data for NYC teachers for several years, and we can look at those scores to see.

Here is one such graph:

That is very close to random.

How about teachers who teach the same subject to two different grade levels (say, fourth-grade math and fifth-grade math)? Again, random points:

One thing that all veteran teachers agree on is that they stunk at their job during their first year and got a lot better their second year. This should show up on value-added graphs of year 1 versus year 2 scores for the same teachers, right?

Wrong.

Take a look:

One last point:

Mayor Gray and chancellors Henderson and Rhee all claim that education in DC only started improving after mayoral control of the schools, starting in 2007.

Graphs and the NAEP show a different story. We won’t know until next week how DCPS and the charter schools did, separately, for 2013, but the following graphs show that reading andmath scores for DC fourth- and eighth-graders have been rising fairly steadily for nearly twenty years, or long before mayoral control or the appointments of our two chancellors (Rhee and Henderson).

Here is another study that shows that Value-Added measurements for teachers are extremely unstable over time. It’s by one Mercedes K. Schneider, and it was done for Louisiana. You can read all of the details yourself. Here I am going to reproduce a couple of the key tables:

and I also quote some of her explanation:

“Each number in the table is a percentage of teachers in the study/actual number of teachers who were first ranked one way using 2008-09 student test scores (reading to the left) then ranked either the same way (bolded diagonal) or a different way (all numbers not bolded) using 2009-10 student test scores (reading at the top). For example, the percentage 4.5% (23 teachers) in Table 6 (immediately above this text) represents the percentage of ELA teachers originally ranked in 2008-09 in the top 91-99% (reading to the left) but reranked in 2009-10 in the bottom 1-10% (reading at the top of the column) given that the teachers changed nothing in their teaching.

.

“Thus, these two tables represent how poorly the standardized tests classify teachers (2008-09) then reclassify teachers (2009-10) into their original rankings. Tables 5 and 6 are a test of the consistency of using standardized tests to classify teachers. It is like standing on a bathroom scale; reading your weight; stepping off (no change in your weight); then, stepping on the scale again to determine how consistent the scale is at measuring your weight. Thus, if the standardized tests are stable (consistent) measures, they will reclassify teachers into their original rankings with a high level of accuracy. This high level of accuracy is critical if school systems are told they must use standardized tests to determine employment and merit pay decisions. I have bolded the cells on the diagonals of both tables to show just how unstable these two standardized tests are at classifying then correctly reclassifying teachers. If the iLEAP and LEAP-21 were stable, then the bolded percentages on the diagonals of both tables would be very high, almost perfect (99%).

.

“Here is what we see from the diagonal in Table 5:

.

“If a math teacher is originally ranked as the lowest, without altering his or her teaching, the teacher will likely be re-ranked in the lowest category only 26.8% of the time. Conversely, without altering his/her teaching, a math teacher ranked as the highest would likely be re-ranked in the highest group only 45.8% of the time even if she/he continued to teach the same way. (…)

“A math teacher originally ranked in the highest category will be re-ranked in the middle category 35.1% of the time and re-ranked in the lowest category 1.8% of the time. These alterations in ranking are out of the teacher’s control and do not reflect any change in teaching. Even though 1.8% might seem low, notice that in the study alone, this represented 8 math teachers, 8 real human beings, who could potentially lose their jobs and face the stigma of being labeled “low

performers.”

.

“As we did for Table 5, let’s consider the diagonal for Table 6:

.

“If an ELA teacher is originally ranked as the lowest, without altering his or her teaching, the teacher will likely be re-ranked in the lowest category only 22.3% of the time. Conversely, without altering his/her teaching, an ELA teacher ranked as the highest would likely be re-ranked in the highest group only 37.5% of the time even if she/he continued to teach the same way. (…)

.

“An ELA teacher originally ranked in the highest category will be re-ranked in the middle category 37.1% of the time and re-ranked in the lowest category 4.5% of the time. These alterations in ranking are out of the teacher’s control and do not reflect any change in teaching.

.

“Even though 4.5% might seem low, notice that in the study alone, this represented 23 ELA teachers who could potentially lose their jobs and face the stigma of being labeled “low performers.” “

———–

Your thoughts? To leave a comment, click on the way-too-tiny “Leave a Comment” button below.

This article is worth reading a couple of times. It makes the point that teachers and their unions need to look into the legal and statistical framework that supposedly upholds Value-Added Methodologies (VAM) and to challenge both.

Like this:

I quote from a paper studying whether value-added scores for the same teachers tend to be consistent. In other words, does VAM allow us a chance to pick out the crappy teachers and give bonuses to the good one?

The answer, in complicated language, is essentially NO, but here is how they word it:

“Recently, a number of school districts have begun using measures of teachers’ contributions to student test scores or teacher “value added” to determine salaries and other monetary rewards.

In this paper we investigate the precision of valueadded measures by analyzing their inter-temporal stability.

We find that these measures of teacher productivity are only moderately stable over time, with year-to-year correlations in the range of 0.2-0.3.”

Or in plain English, and if you know anything at all about scatter plots and linear correlation, those scores wander all over the place and should never be used to provide any serious evidence about anything. Speculation, perhaps, but not policy or hiring or firing decisions of any sort.

They do say that they have some statistical tricks that allow them to make the correlation look better, but I don’t trust that sort of thing. It’s not real.

Here’s a table from the paper. Look at those R values, and note that if you squared those correlation constants (go ahead, use your calculator on your cell phone) you get numbers that are way, way smaller – like what I and Gary Rubenstein reported concerning DCPS and NYCPS.

For your convenience, I circled the highest R value, 0.61, in middle schools on something called the normed FCAT-SSS, whatever that is (go ahead and look it up if it interests you) in Duval county, Florida, one of the places where they had data. I also circled the lowest R value, 0.07, in Palm Beach county, on the FCAT-NRT, whatever that is.

I couldn’t resist, so 0.56^2 is about 0.31 as an r-squared, which is moderate. There is only one score anywhere near that high 0.56, out of 24 such correlation calculations. The lowest value is 0.07 and if we square that and round it off we get an r-squared value of 0.005, shockingly low — essentially none at all.

The median correlation constant is about 0.285, which I indicated by circling two adjacent values of 0.28 and 0.29 in green. If you square that value you get r^2=0.08, which is nearly useless. Again.

I’m really sorry, but even though this paper was published four years ago, it’s still under wraps, or so it says?!?! I’m not supposed to quote from it? Well, to hell with that. it’s important data, for keereissake!

The title and authors are as follows, and perhaps they can forgive me. I don’t know how to contact them anyway. Does anybody have their contact information? Here is the title, credits, and warning:

*This paper has not been formally reviewed and should not be cited, quoted, reproduced, or retransmitted without the authors’ permission. This material is based on work supported by a supplemental grant to the National Center for Performance Initiatives funded by the United States Department of Education, Institute of Education Sciences. Any opinions, findings and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of these organizations.

“DCPS analyzed the relationship between TLF rubric scores and individual teacher value-added scores based on the DC-CAS.

“At this early stage in the use of value-added analysis nationally, the hope is that there is a strong correlation between a teachers’ score on an instructional rubric and his or her value-added score. This would validate the instructional rubric by showing that doing well in instruction produces better student outcomes. DCPS analysis at the end of the first year of IMPACT suggests that there is a modest correlation between the two ratings (0.34).

DCPS’s correlations are similar to those of other districts that are using both an instructional rubric and value-added data. A moderate correlation suggests that while there is a correlation between the assessment of instruction and student learning as measured by standardized tests (for the most part), it is not strong. At this early stage of using value-added data this is an issue that needs to be further analyzed.”

Ya know, if if the educational Deformers running the schools today were honest, they would admit that they’re still working the bugs and kinks out of this weird evaluation system. They would run a few pilot studies here or there, no stakes on anyone, so nobody cheats, and see how it goes. Then either revise it or get rid of it entirely.

Instead, starting in Washington, DC just a few years ago, with Michelle Rhee and Adrian Fenty leading the way locally and obscenely rich financiers funding the entire campaign, they rushed through an elaborate system of secret formulas and rigid rubrics, known as IMPACT. It appears that their goal of demoralizing teachers and convincing the public that public schools need to be closed and be turned over to the same hedge fund managers that brought us the current Great Depression, high unemployment rates, foreclosures. While the gap between the very wealthiest and the rest of the population, especially the bottom 50%, has become truly phenomenal.

Here’s a little table from the report, same page:

(Just so you know, I’ve been giving r^2 in my previous columns, not r. I believe they are using r; to compare that to my previous analyses, if you take 0.34 and square it, you get about 0.1156. That means that the IVA “explains” about 12% of the TLF, and vice versa. Pretty weak stuff.

Would I be alone in suggesting that the “hope” of a strong correlation has not been fulfilled? In fact, I think that’s a pretty measley correlation, and it suggests to me the possibility that neither the formal TLF evaluation rubrics done by administrators, nor the Individual Value-Added magic secret formulas, do an adequate or even competent job of measuring the output of teachers.

You really need to read this article in today’s Washington Post, by Bill Turque. It describes the situation of Sarah Wysocki, a teacher at MacFarland, who was given excellent evaluations by her administrators during her second year; but since her “Value-Added” scores were low for the second year in a row, she was fired.

Ms. Wysocki raises the possibility that someone cheated at Barnard, the school where a lot of her students had attended the previous year; she said that there were students who scored “advanced” in reading who could, in fact, not read at all.

Curious, I looked at the OSSE data for Barnard and found that the percentages of “advanced” students in grades 3 and 4 had what looks to me to be some rather suspicious drops from SY2009-10 to SY 2010-2011, at a school that apparently has a 70% to 80% free-or-reduced-price lunch population:

Grade 3, reading, 2010: 11% “advanced” but only 3% the next year;

Grade 4, reading, 2010: 29% “advanced”, but only 7% the next year.

Ms. Wysocki raised the accusation of cheating, but, as usual, DCPS administration put a bunch of roadblocks in the way and deliberately failed to investigate.

And naturally, Jason Kamras thinks he’s doing a peachy job and that there is nothing wrong with IMPACT or DC’s method of doing value-added computations.

Gary Rubenstein has two excellent posts where he analyzes what happened with the New York Public School System’s value-added measurements for teachers, which were just released.

He discovered several very important things:

(1) There is almost no correlation between a teacher’s score in 2009 to that for the following year.

(2) There is almost no correlation between a teacher’s score when teaching math and when teaching reading – to the same kids, the same year, and in the same elementary class.

(3) There is almost no correlation between a teacher’s score when teaching different grade levels of the same subject (i.e., Math 6 versus Math 7, and so on).

In other words, the Value Added Methodology is very close to being a true random number generator — which would be great if we were playing some sort of fantasy role-playing game or a board game like Monopoly or Yahtzee. But it’s an utterly ridiculous way to run a school system and to evaluate teachers.